RG resummation effects are more interesting in the case where the decaying heavy resonance is charged under the SM gauge group. We now discuss this for the case of the operators appearing at leading order in power counting. Their anomalous dimensions can be derived from a two-loop master formula for the anomalous dimensions of scattering amplitudes containing both massless and massive partons derived in Refs. [1]}, [2]}, [3]}, [4]}. We find that
\(\mathbf {\Gamma }_{Q_L Q_L}(\mu )&= \left( \frac{1}{36}\,\gamma _{\rm cusp}^{(1)} + \frac{3}{4}\,\gamma _{\rm cusp}^{(2)}- \frac{1}{6}\,\gamma _{\rm cusp}^{(3)} \right) \left( \ln \frac{m_G^2}{\mu ^2} - i\pi \right)+ \frac{3}{2}\,\gamma _{\rm cusp}^{(3)}\,\ln \frac{m_G^2}{\mu ^2} + \gamma ^{G^{\prime }}+ \lbrace  \mathbf {\gamma }^{Q_L},\,.\, \rbrace  \,,\\\mathbf {\Gamma }_{q_R q_R}(\mu )&= \left( e_q^2\,\gamma _{\rm cusp}^{(1)} - \frac{1}{6}\,\gamma _{\rm cusp}^{(3)} \right)\left( \ln \frac{m_G^2}{\mu ^2} - i\pi \right)+ \frac{3}{2}\,\gamma _{\rm cusp}^{(3)}\,\ln \frac{m_G^2}{\mu ^2} + \gamma ^{G^{\prime }}+ \lbrace  \mathbf {\gamma }^{q_R},\,.\, \rbrace  \,;\quad q=u,d , \\\mathbf {\Gamma }_{GB}(\mu )&= \frac{3}{2}\,\gamma _{\rm cusp}^{(3)}\,\ln \frac{m_G^2}{\mu ^2} + \gamma ^{G^{\prime }} + \gamma ^G + \gamma ^B \,.\) 
